The former professional, who was as high as number 10 in the world at one stage in his career, had to win three matches to move on.
After beating from Irish professional David Morris 5-1 on Thursday, he then enjoyed a 5-2 victory over Stephen Rowlings on Friday afternoon and followed it up with a 5-1 reversal of Les Dodd later in the day.
The Northern Irishman has reached the World Championship semis twice - in 2000 and 2001 - and the last 16 a further four times.
He still needs to win another four matches though if he is to return to the Crucible though, starting with a match against India's Pankaj Advani in what is the fifth of eight qualification rounds.
Among the bigger names entering qualification at round five are Tony Drago and Belgian youngster Luca Brecel.
The likes of Jimmy White, James Wattana, Alan McManus and Barry Pinches then enter in round six.
Qualification round four
Justin Astley 5 - 2 Patrick Wallace
Joe Swail 5 - 1 Les Dodd
Qualification round three
Patrick Wallace 5 - 1 Tony Chappel
Les Dodd 5 - 1 Andrew Norman
Justin Astley 5 - 2 Paul Wykes
Joe Swail 5 - 2 Stephen Rowlings
- Sports & Recreation
- Stephen Rowlings